1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Zero group refractive index

  1. May 10, 2016 #1
    1. The problem statement, all variables and given/known data.
    I am attempting to determine the group refractive index of a laser cavity at it's resonance frequency.

    2. Relevant equations.
    \begin{align*}
    \frac{2\omega n L}{c} &= 2m\pi
    \end{align*}

    \begin{align*}
    n_g &= n + \omega \frac{dn}{d\omega}
    \end{align*}

    3. The attempt at the solution.
    I have considered a uniform plane wave propagating within the cavity satisfying the following relation
    \begin{align*}
    \frac{2\omega n L}{c} &= 2m\pi
    \end{align*}
    where ω is the angular frequency, n is the effective refractive index and L is the length of the laser cavity. I have derived the group refractive index as follows
    \begin{align*}
    n_g &= n + \omega \frac{dn}{d\omega} \\
    &= \frac{c m \pi}{\omega L} - \frac{c m \pi}{ \omega L}\\
    &= 0
    \end{align*}

    If this is correct, I don't understand what this is physically entailing. Any insight would be much appreciated! Thank you.
     
  2. jcsd
  3. May 11, 2016 #2

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    You are calculating the group index of refraction for a monochromatic wave, which is of course zero.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Zero group refractive index
Loading...